Related papers: A lasso for hierarchical interactions

Based on technological advances in sensing modalities, randomized trials with primary outcomes represented as high-dimensional vectors have become increasingly prevalent. For example, these outcomes could be week-long time-series data from…

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…

The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

While Weighted Lasso sparse regression has appealing statistical guarantees that would entail a major real-world impact in finance, genomics, and brain imaging applications, it is typically scarcely adopted due to its complex…

Vector autoregression (VAR) models are widely used to analyze the interrelationship between multiple variables over time. Estimation and inference for the transition matrices of VAR models are crucial for practitioners to make decisions in…

The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…

A method of `network filtering' has been proposed recently to detect the effects of certain external perturbations on the interacting members in a network. However, with large networks, the goal of detection seems a priori difficult to…

Many problems in classification involve huge numbers of irrelevant features. Model selection reveals the crucial features, reduces the dimensionality of feature space, and improves model interpretation. In the support vector machine…

We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that…

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure,…

In Compressed Sensing and high dimensional estimation, signal recovery often relies on sparsity assumptions and estimation is performed via $\ell_1$-penalized least-squares optimization, a.k.a. LASSO. The $\ell_1$ penalisation is usually…

Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…

High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…